Erweitertes Heronverfahren
Author: Prof. Dr. Dörte Haftendorn
Date: Okt 2004

Die Rechtecke haben alle Flächeninhalt 2

Erweitertes Heronverfahren

heron(x)=\frac{1}{2} (x+ \frac{a}{x^{r-1}})

Ha 04

k = 2
R = Point(xAxis)
r: x(R)
heron(x) = (x + r / x^(k - 1.0)) / 2.0
wh(x) = x
Start = Point(xAxis)
c = OrthogonalLine(Start, xAxis)
B = Intersect(heron, c, (3.0, 1.8333333333333333))
d = OrthogonalLine(B, yAxis)
C = Intersect(wh, d)
e = OrthogonalLine(C, xAxis)
D = Intersect(heron, e, (1.8333333333333333, 1.4621212121212122))
f_2 = Segment(Start, B)
g = Segment(B, C)
h = Segment(C, D)
i = OrthogonalLine(D, yAxis)
E = Intersect(wh, i)
j = OrthogonalLine(E, xAxis)
F = Intersect(heron, j, (1.4621212121212122, 1.414998429894803))
k_1 = OrthogonalLine(F, yAxis)
G = Intersect(wh, k_1)
l = OrthogonalLine(G, xAxis)
H = Intersect(heron, l, (1.414998429894803, 1.4142137800471977))
m = OrthogonalLine(H, yAxis)
I = Intersect(wh, m)
n = OrthogonalLine(I, xAxis)
J = Intersect(heron, n, (1.4142137800471977, 1.4142135623731118))
p = OrthogonalLine(J, yAxis)
K = Intersect(wh, p)
b = Segment(Start, B)
q = Segment(B, C)
s = Segment(C, D)
t = Segment(D, E)
a_1 = Segment(E, F)
b_1 = Segment(C, D)
c_1 = Segment(F, G)
d_1 = Segment(G, H)
e_1 = Segment(H, I)
f_1 = Segment(I, J)
g_1 = Segment(J, K)
h_1 = OrthogonalLine(K, xAxis)
Letzter = Intersect(heron, h_1, (1.4142135623731118, 1.414213562373095))
i_1 = Segment(K, Letzter)
f(x) = 2.0 / x
L = Intersect(f, f_2, (3.0, 0.6666666666666666))
C': (x(C), 2.0 / x(C))
C'': (x(C), 0.0)
O = (0, 0)
C''': (0.0, y(C'))
Vieleck1, o, c'', c', c''' = Polygon(O, C'', C', C''')
L''': (0.0, y(L))
Vieleck2, o_1, start, l_1, l''' = Polygon(O, Start, L, L''')
E': (x(E), 2.0 / x(E))
E'': (x(E), 0.0)
E''': (0.0, y(E'))
Vieleck3, o_2, e'', e', e''' = Polygon(O, E'', E', E''')
A = Point(wh)
A': (x(A), 2.0 / x(A))
M = Midpoint(A, A')
Text2: heron + ""